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Mirrors > Home > MPE Home > Th. List > Mathboxes > ismndo | Structured version Visualization version Unicode version |
Description: The predicate "is a monoid". (Contributed by FL, 2-Nov-2009.) (Revised by Mario Carneiro, 22-Dec-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ismndo.1 |
Ref | Expression |
---|---|
ismndo | MndOp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mndo 33666 | . . 3 MndOp | |
2 | 1 | eleq2i 2693 | . 2 MndOp |
3 | elin 3796 | . . 3 | |
4 | ismndo.1 | . . . . 5 | |
5 | 4 | isexid 33646 | . . . 4 |
6 | 5 | anbi2d 740 | . . 3 |
7 | 3, 6 | syl5bb 272 | . 2 |
8 | 2, 7 | syl5bb 272 | 1 MndOp |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 cin 3573 cdm 5114 (class class class)co 6650 cexid 33643 csem 33659 MndOpcmndo 33665 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-dm 5124 df-iota 5851 df-fv 5896 df-ov 6653 df-exid 33644 df-mndo 33666 |
This theorem is referenced by: ismndo1 33672 |
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